The below law will discuss the order of handing over the cup from one hand to the other when washing hands upon awakening. With which hand should one begin the washing? Should one hand over the cup from the right hand to the left hand and from the left-hand to the right hand? Prior to entering this discussion in B, we will first explain in A the general requirement to pour the water onto the hands inconsecutively by the morning washing.
Washing each hand three times and alternating hands between each pouring: The Talmudic sages stated that the impurity does not [completely] leave ones hands until one pours water on each hand three times. The sages [of Kabala] received a tradition that the three pourings on each hand [must] be done inconsecutively [in order to completely remove all remnant of the impurity from ones hands]. [Thus one must be very careful to pour the water on each hand inconsecutively even Bedieved.]
B. The law:
Handing the vessel from the left hand to the right hand: After pouring one time on the right hand, one then takes the vessel into his right hand and pours one time on his left hand, and then repeats this for a total of three pourings on each hand. Some people however are careful to never hand the cup of water from the left hand to the right hand and hence they first put the basin down and then take it with the right hand. However they make sure to directly hand it from the right hand to the left hand when it comes the turn for the water to be poured on the right hand.
Which hand is a lefty to pour on first?
If another person is pouring on one’s hand from which hand should he pour?
He should pour using his right hand being that the right side represents mercy.
 Admur Basra 4:2; Tractate Shabbos 109a
 Admur Basra 4:2. This implies that even one pouring removes some part of the impurity. [Ketzos Hashulchan 2 footnote 11]
 Admur Kama 4:4, Basra 4:2, Siddur; Igros Kodesh Rebbe Rayatz 1:100
Other Opinions-Pouring four times: Some Poskim rule that one is to pour four times on each hand. [Gr”a; Kav Yashar 13; Darkei Chaim Veshalom 2] The reason for doing so is because they hold the water of the third washing is impure and hence needs to be washed off with a fourth washing. This custom is brought down in many Sefarim of Minhagim and is followed by many, and so is the proper custom to follow. [Kaf Hachaim 4:8; Piskeiy Teshuvos 4:7 footnote 87] However this is not the custom of Chabad Chassidim and rather we specifically wash only three times on each hand. [Igros Kodesh Rebbe Rayatz 1:100]
 Siddur; Shaar Hakavanos of Arizal; Peri Eitz Chaim 3; Matza Shemura 3 [brought in Kaf Hachaim 4:12]; In Basra 4:2 it is implied that this applies also according to the Sages of the Talmud, although in truth one can read it differently. In Ketzos Hashulchan 2 footnote 11 he writes that according to the Talmud inconsecutive pourings are not needed to remove the impurity. In Kama 4:4 no mention is made regarding who instituted the inconsecutive pourings.
 Siddur and Basra 4:2; Kama 4:4 mentions this as a separate point, without stating that if done consecutively that the impurity will not be removed. Regarding if one may make a blessing if he washed consecutively and no longer has anymore water to wash with-See Q&A below!
 Siddur and Basra 4:2; This implies that even one pouring removes some part of the impurity. See Chapter 3 Halacha 7B that in such a case one is no longer liable to beware of the Kabalistic restrictions that apply prior to washing although he is to be stringent regarding the Talmudic restrictions due to doubt.
 Admur Basra 4:2, Siddur; Kama 4:4: “One should not pour on his hands three times consecutively, rather he is to pour once on the right and once on the left and so on and so forth for a total of three times.”; Arizal in Shaar Hakavanos based on Zohar; Olas Tamid 17; Beis Oveid 4; Ben Ish Chaiy Toldos 1
Other Opinions: Some Poskim rule one is to pour three times consecutively on each hand. [Kneses Hagedola; Seder Hayom; Elya Raba 4:5; See Artzos Chaim 10] Some rule that one who desires to be stringent like both opinions is to pour three times consecutively and then pour another two times inconsecutively on each hand. [Zachor Leavraham 1:50; Chesed Lialafim; Artzos Chaim brought in Yifei Laleiv 1:7, brought in Kaf Hachaim 4:12; Likkutei Mahrich] Alternatively one is to pour three times consecutively and then three times inconsecutively. [Kaf Hachaim 4:12; Yaavetz in Siddur; Kaf Hachaim [Falagi] 18:22; Yifei Laleiv ibid; Mishmeres Shalom 1:5] Practically the main opinion follows the Arizal that once one has poured three times inconsecutively all the impurity has left. [Kaf Hachaim 4:12; See Piskeiy Teshuvos 4:7 footnotes 79-80]
 Siddur; Vetzaruch Iyun on the meaning of Bedieved, as in the Siddur Admur rules that if one does not have enough water to wash three times then washing one time suffices and he is to say a blessing. Perhaps however this means that the Talmudic restrictions still apply.
 Admur Kama 4:10; Siddur; Seder Netilas Yadayim 5
 The reason: The reason for giving the right side precedence is because we find that the Torah gives the right side importance regarding the service in the Temple, anointing of the Levim, purification of the Metzora, and Chalitza. [Basra 2:4; Kama 2:4]
 Admur Kama 4:10; Siddur; Seder Netilas Yadayim 5; Seder Hayom; Shaar Hakavanos of Arizal brought in Kaf Hachaim 4:12
 Siddur; In Kama 4:10 Admur writes “It is a good thing”
 The reason: Although the right hand needs to be washed prior to the left, being that we always give precedence to the right, nevertheless one is to first place the cup in the right hand and then give it to the left for the reason written in the Zohar. [Kama 4:10; Seder Netilas Yadayim 5] One is to intend that everything is included in the right side and from the right it comes to the left. [Kama 2:3] Seder Hayom: “One is to take the vessel in his right hand in order to draw down waters of kindness to purify himself with”; See also Igros Kodesh Rebbe Rayatz 1:100: “In order to fulfill both the taking and the pouring with the right hand. In additional intent is because all the Hashpaos come from the right and especially Netilas Yadayim which is an Hamshacha of Mochin in Midos and the gate of this is the right”
 Ketzos Hashulchan 2:3
 Ben Ish Chaiy Toldos 1; Kaf Hachaim 4:13
The reason: The reason for this is to show that the right is a master to the left. [Poskim ibid]
 Peri Megadim 158 A”A 1; M”B 4:22 in name of Artzos Hachaim; Amudei Hashulchan 2:2; Kaf Hachaim 4:35; See also Igros Kodesh Rebbe Rayatz 1:100; Miasef Lekol Hamachanos 4:53; Beir Moshe 2:1
 As one should pour from the right which is Chesed over the left which is Gevurah and hence overcome the Gevuros. [ibid; Seder Hayom based on Zohar]
 Tzemach Tzedek Orach Chaim 4:6 and 5:8 based on Admur 183:7 that a lefty is to hold the Kos Shel Bracha in his left hand; 651:14 that a lefty is to hold the Lulav in his left hand; Siddur Shaar Menachem [Rabbi Levi Bistritzky]; See Sefer Dinei Iter p. 51-54
 Elya Raba 4:5 brought in Kaf Hachaim 4:36